Problem: $ C = \left[\begin{array}{rrr}4 & -1 & 0 \\ -1 & 0 & -2 \\ 2 & 3 & -2\end{array}\right]$ $ D = \left[\begin{array}{rrr}3 & 0 & 1 \\ 2 & 3 & 3 \\ 2 & -2 & 2\end{array}\right]$ Is $ C- D$ defined?
In order for subtraction of two matrices to be defined, the matrices must have the same dimensions. If $ C$ is of dimension $( m \times  n)$ and $ D$ is of dimension $( p \times  q)$ , then for their difference to be defined: 1. $ m$ (number of rows in $ C$ ) must equal $ p$ (number of rows in $ D$ ) and 2. $ n$ (number of columns in $ C$ ) must equal $ q$ (number of columns in $ D$ Do $ C$ and $ D$ have the same number of rows? Yes Yes No Yes Do $ C$ and $ D$ have the same number of columns? Yes Yes No Yes Since $ C$ has the same dimensions $(3\times3)$ as $ D$ $(3\times3)$, $ C- D$ is defined.